Average Error: 0 → 0
Time: 4.8m
Precision: 64
\[2 \cdot \left(\left(1 \cdot \frac{1}{9} + \frac{1}{9} \cdot \frac{1}{9}\right) + \frac{1}{9} \cdot 1\right)\]
↓
\[\mathsf{fma}\left(2, 1, \frac{1}{9}\right) \cdot \left(\frac{1}{9} \cdot 2\right)\]
2 \cdot \left(\left(1 \cdot \frac{1}{9} + \frac{1}{9} \cdot \frac{1}{9}\right) + \frac{1}{9} \cdot 1\right)
↓
\mathsf{fma}\left(2, 1, \frac{1}{9}\right) \cdot \left(\frac{1}{9} \cdot 2\right)
double f() {
        double r8601528 = 2.0;
        double r8601529 = 1.0;
        double r8601530 = 9.0;
        double r8601531 = r8601529 / r8601530;
        double r8601532 = r8601529 * r8601531;
        double r8601533 = r8601531 * r8601531;
        double r8601534 = r8601532 + r8601533;
        double r8601535 = r8601531 * r8601529;
        double r8601536 = r8601534 + r8601535;
        double r8601537 = r8601528 * r8601536;
        return r8601537;
}
↓
double f() {
        double r8601538 = 2.0;
        double r8601539 = 1.0;
        double r8601540 = 9.0;
        double r8601541 = r8601539 / r8601540;
        double r8601542 = fma(r8601538, r8601539, r8601541);
        double r8601543 = 2.0;
        double r8601544 = r8601541 * r8601543;
        double r8601545 = r8601542 * r8601544;
        return r8601545;
}

Error

Target

Original0
Target0
Herbie0
\[\left(\left(\frac{1}{9} \cdot 1\right) \cdot 2 + 2 \cdot \left(\frac{1}{9} \cdot \frac{1}{9}\right)\right) + 2 \cdot \left(1 \cdot \frac{1}{9}\right)\]

Derivation

  1. Initial program 0

    \[2 \cdot \left(\left(1 \cdot \frac{1}{9} + \frac{1}{9} \cdot \frac{1}{9}\right) + \frac{1}{9} \cdot 1\right)\]

  2. Simplified0

    \[\leadsto \color{blue}{\mathsf{fma}\left(2, 1, \frac{1}{9}\right) \cdot \left(\frac{1}{9} \cdot 2\right)}\]

  3. Final simplification0

    \[\leadsto \mathsf{fma}\left(2, 1, \frac{1}{9}\right) \cdot \left(\frac{1}{9} \cdot 2\right)\]

Reproduce

herbie shell --seed 2019174 +o rules:numerics
(FPCore ()
  :name "Rectangular parallelepiped of dimension a×b×c"

  :herbie-target
  (+ (+ (* (* (/ 1.0 9.0) 1.0) 2.0) (* 2.0 (* (/ 1.0 9.0) (/ 1.0 9.0)))) (* 2.0 (* 1.0 (/ 1.0 9.0))))

  (* 2.0 (+ (+ (* 1.0 (/ 1.0 9.0)) (* (/ 1.0 9.0) (/ 1.0 9.0))) (* (/ 1.0 9.0) 1.0))))